Navigation data for a moving platform, such as a ship, includes current position and velocity. Attitude data includes orientation (i.e., roll, pitch and heading measurements) and orientation rate of the platform in a reference frame. Measurements of a tracked target may be used by multiple processing functions and may generally involve transformation from the platform's coordinate system to an external coordinate system.
This transformation matrix is a function of roll, pitch, and heading of the platform's orientation with respect to the East, North, and Up (ENU) coordinate frame. These angular orientations are measured by component gyroscopes of an inertial measurement unit IMU For example, an inertial measurement unit (IMU) of the INS may contain three single-axis accelerometers and three gyroscopes, where, for example, each gyroscope is a single degree of freedom (SDOF) ring laser gyroscope (RLG). A single-axis accelerometer mounted on a moving platform measures linear acceleration experienced along its measurement axis. The three single-axis accelerometers are mounted on three mutually orthogonal axes. These three mutually orthogonal axes define the coordinate frame of the IMU. This frame is aligned to the platform by physically aligning the three orthogonal axes of the IMU to the three orthogonal axes of the platform. This allows accelerations measured by the IMU in each axis to constitute an acceleration vector of the platform. The accelerometers need the three RLGs to measure the orientation of the platform with respect to ENU fixed coordinate frame. Thus, the IMU provides both the linear acceleration of the platform and the angular orientations (e.g. roll, pitch, heading turns). With reference to an initial position and attitude, the IMU provides the information about the current position, velocity, and attitude of the platform, allowing the platform to set and adjust its course and determine the location of any other objects that are being tracked and/or targeted by the platform.
The accelerometer measurements provide an acceleration vector with respect to the inertial frame of the IMU. In order to relate the accelerometer measurements to an Earth frame, the angular orientation of the accelerometer assembly with respect to the Earth is determined. For example, by integrating the acceleration vector twice, the position of the IMU can be obtained. This position can be converted to latitude and longitude with reference to an Earth model, e.g., World Geodetic System, revision 84 (WGS-84). The angular orientation of the IMU is measured by mounting the three RLGs on the three planes defined by the mutually orthogonal axes used for the accelerometers. The acceleration of the platform is measured by the IMUs with respect to the instantaneous ENU coordinate frame, which is referenced by the navigation data to the Earth Centered Earth Fixed (ECEF) coordinate frame of WGS-84. This acceleration vector is fed back to the computation of the velocity and position of the IMU, with respect to WGS-84. The SDOF RLG detects angular rotation around the axis normal to the plane containing the RLG. This provides the angular orientation of that axis.
These sensing elements (RLGs and accelerometers) are mounted on a sensor block assembly, which is mounted within a two-axis (dual axis) gimbal assembly. This dual axis gimbal assembly allows the axes for each RLG and accelerometer to be periodically reoriented during operation. This is accomplished by an inner gimbal that provides rotation in heading and an outer gimbal that allows rotation in roll. This periodic change of orientation allows the cumulative effects of small drift errors in the RLGs and accelerometers to cancel out.
The RLGs and accelerometers are subject to many sources of error. These include but are not limited to, random-walk error, gyro bias error, gyro scale factor error and accelerometer bias. Some of these errors lead to the bias of the output of RLGs and accelerometers. These biases lead to erroneous values for the orientation and position of the sensor block assembly. By reversing the orientation of the sensor block assembly periodically (e.g., every five minutes), a bound is imposed on the biases output from the RLGs and accelerometers.
This periodic reversal of the sensor axes is called indexing. In one example, the rotation of the gimbal assembly takes ten seconds to complete and occurs every five minutes. The orientation of the sensor block is held for five minutes (minus the 10 second rotation duration), therefore retaining the RLG and accelerometer biases with respect to the orientation of the axis being measured. The reorientations of the sensor block assembly change the magnitude and direction of the RLG and accelerometer biases, thereby, canceling out any cumulative effects due to the instrument biases. Indexing gives the IMU a capability to meet a better positional accuracy over a required time period, at the price of introducing a periodically varying mechanical positioning error in attitude.
FIG. 1 is a diagram showing a forward (FWD) and corresponding, aftward (AFT) IMU gyro attitude (either roll, pitch or yaw) angle output, compared to the (assumed, here, constant) truth attitude value. The true attitude angle θ is depicted by the dashed line, trace 105. Traces 100 and 102 are examples of attitude angle measurement produced by the FWD IMU gyroscopes (FWD gyro) and AFT IMU gyroscopes (AFT gyro), respectively. The traces 100, 102 can differ from the true attitude angle trace 105 by mean gyro attitude angle mean traces 101 and 103 from the true attitude. The difference between traces 100 and 101 and the difference between traces 101 and 103 are intended to show errors (biases) due to indexing. This indexing bias is piecewise constant for the interval defined by the indexing times. The transition between indexing biases is shown as instantaneous steps in the traces 100, 102. The idealized step function (to simplify initial presentation) transitions of the angular measurements due to indexing occur at the vertical dashed lines. These vertical dashed lines represent the times of indexing for the FWD and AFT gyros denoted by tif, i=1, 2, 3, . . . and tia, i=1, 2, 3, . . . respectively. Compensation for indexing errors in gyro output traces, 100 and 102, from the mean gyro attitude traces 101 and 103, respectively is desired. Compensation or correction of the mean gyro attitude traces 101 and 103, to the true attitude angle trace 105, requires reference to measurements external to the IMU platform, and is addressed herein. Such a process takes a longer period to resolve than the indexing period. The indexing biases slow convergence of such a process and are a remaining error in the attitude output. Attitude angle measurements of the AFT gyro are subtracted from the attitude angle measurements of the FWD gyro and this difference is plotted as curve 200 in FIG. 2A. The observed difference can be positive or negative and the transitions occur at the times of index.